We consider two models of influence diffusion, namely the independent cascade (IC) and weighted cascade (WC) models [1]}, [2]}, [3]}.
Let us denote \(A_{u,v}\)  as the event that a node \(u\)  successfully activates another node \(v\)  in the diffusion process.
In the IC model, each edge \((u, v)\) , incident to nodes \(u\)  and \(v\) , is associated with a uniform diffusion probability \(p(A_{u,v})\)  that represents the chance that the influenced node \(u\)  successfully activates node \(v\) .
In the WC model, this probability is modulated by the in-degree of node \(v\) , denoted as \(d_v\) , i.e., each edge from node \(u\)  to \(v\)  is assigned a probability \(\frac{1}{d_v}\)  of activating \(v\) .
As in many previous studies [3]}, [5]}, [6]}, we assume that the diffusion process unfolds deterministically in discrete time steps. That is, the influence propagation occurs only once for each edge; this edge will not be used in the future spread of influence; and influenced nodes remain active during the whole diffusion process.
